How do you find the rule for a function machine?

For example:

What is the rule? Prove it!

7 19

16In rule Out

4

In this lesson you will learn how to find the rule for a

function machine by using a vertical table.

Let’s ReviewLet’s Review

+ 2+ 2+ 2

Pattern: Things that are arranged by a certain rule or a set of rules.

The rule shows a common difference in the pattern.

2, 4, 6, 8, 10…

+ 2Rule

2x1 2x2 2x3 2x4 2x5

12 3 4 5

Let’s ReviewLet’s ReviewHow Does a Function Machine Work?

In rule Out5 =10=10 =10

OutIn

5 5 ?=+-÷X

Rule ?

Let’s ReviewA Common MistakeWhen looking at a function machine,

don’t stop at just one input or output.

Input three or four numbers to prove the rule works on all the input numbers.

Let’s ReviewCore LessonFind the rule

Input RULE Output

7 35

8 40

In rule Out

4 20

+?x 5?x 5

x 5

5 256 x 5 30

Features

+ 5

+ 5

+ 5

+ 5

x 5

x 5x 5

In Out

Let’s ReviewCore LessonWhat is the rule?

In Rule Out

4 16

7 19

Input Rule Output

4 16

6 18

X 4 ?+ 12 ?+ 12

+ 12+ 125 17

+ 127 19

+1+1+1

+1+1+1

+ 12

Input + 12

In this lesson you learned how to find the rule for a function machine by using a vertical

table.

Let’s ReviewGuided PracticeWhat is the rule?

In Rule Out4 363 27

Input RULE Output

3 27

4 36+ 24 ?x 9x 9x 95 45

x 92 18x 91 9

+1+1+1+1

+9+9+9+9

X 9

Input X 9

Let’s ReviewGuided PracticeWhat is the rule? Solve for the

missing output numbers.

In Rule Out

In RULE Out

1

3 18

4 19

5

6

X6 ?

+15 ?+15

+15

+15

+15

+15

16

20

21

+15

Let’s ReviewExtension ActivitiesFind the rule for the pattern. Solve for the

missing in or output.

In Rule Out

In RULE Out

? ?

2 14

3 ?

? 28

5 ?

Let’s ReviewExtension ActivitiesFind the rule and the missing input and

output numbers.

In Rule Out

In RULE Out

? 7

2 12

3 17

? ?

5 27

Let’s ReviewQuick Quiz

What is the rule?

What is the rule?

In Rule Out

In Rule Out

5

10

5

6

10

15

11

17

A) +2 B) +5C) x2 D)

x5

A) x1 B) -2C) x2 D)

+6